Multiple component codes based generalized low-density parity-check codes for high-speed optical transport

ABSTRACT

Systems and methods for data transport, including encoding streams of input data using generalized low-density parity check (GLDPC) encoders, the one or more GLDPC encoders being configured to generate GLDPC coded data streams using a plurality of component local codes to improve error correction strength, employ single-parity checks and two or more local block codes during generation of the GLDPC codes, and enable continuous tuning of code rate using the generated GLDPC codes. Signals may be generated using mappers, the mappers configured to assign bits of signals to signal constellations and to associate the bits of the signals with signal constellation points. The signal may be modulated using an I/Q or 4-D modulator composed of one polarization beam splitter, two I/Q modulators, and one polarization beam combiner. The modulated signals are multiplexed using a mode-multiplexer, transmitted over a transmission medium, and the signals are received and decoded using GLDPC decoders.

RELATED APPLICATION INFORMATION

This application claims priority to provisional application Ser. No.61/890,445 filed on Oct. 14, 2013, incorporated herein by reference.

BACKGROUND

Technical Field

The present invention relates to coded modulation, and moreparticularly, to generalized low-density parity-check (GLDPC) codesderived from multiple component codes suitable for ultra-high-speedserial optical transport networks.

Description of the Related Art

The 40/100 Gigabit Ethernet standard (e.g., IEEE 802.3ba) has recentlybeen ratified, but there exists ever-increasing capacity demands (e.g.,future Terabit per second Ethernet, TbE). As the operating symbol ratesincrease, the deteriorating effects of fiber nonlinearities andpolarization-mode dispersion (PMD) reach levels that inhibit reliablecommunication over the optical fiber network. Thus solutions for 100 GbEand beyond need to attain ultra-high transmission speeds in terms ofaggregate bit rates while keeping the operating symbol rates low tofacilitate nonlinearity and polarization mode dispersion (PMD)management. This in return requires the use of modulation formats withhigh spectral efficiencies (SE).

However, as a signal constellation grows in size to increase its SE, sodoes the optical signal-to-noise ratio (OSNR) it requires to achieve acertain bit error ratio (BER) and this might jeopardize its use inpractice, but when used in combination with strong forward errorcorrection (FEC) codes, the OSNR requirement of the systems employingsuch high-SE modulation formats can be significantly lowered. Thus,methods that can combine modulation and coding (e.g., coded modulationmethods), are useful in the design and implementation of high-speedoptical communication systems. Furthermore, in the context of high-speedoptical communication systems, not only the error correction performancebut also the complexity of a coded modulation system plays a crucialrole.

A key enabling technology for the next generation of optical transportis a soft-decision forward error correction (FEC). It has been shownthat LDPC coded modulation based on large girth (e.g., ≧10) LDPC codesprovide excellent bit error rate (BER) performance, but the codewordlengths are excessively long for quasi-cyclic (QC) LDPC code design, andcorresponding decoders are difficult to implement with existinghardware, and girth-8 LDPC codes exhibit the error floor phenomenon. Toeliminate the error floor phenomenon, an outer BCH/RS code has beentraditionally used. By using this approach the error floor of girth-8and girth-6 LDPC codes can be eliminated. However, the corresponding netcoding gains (NCGs) are much below that of large-girth LDPC codes.

SUMMARY

A method for data transport, including encoding one or more streams ofinput data using one or more generalized low-density parity check(GLDPC) encoders, the one or more GLDPC encoders being configured togenerate GLDPC coded streams using a plurality of component local codesto increase error correction strength; employ single-parity checks andtwo or more local block codes during generation of the GLDPC codes; andenable continuous tuning of code rate using the generated GLDPC codes;generating one or more signals using one or more mappers, the mappersconfigured to assign bits of one or more signals to one or more signalconstellations and to associate the bits of the one or more signals withone or more signal constellation points; modulating the signal frommapper using either I/Q or 4-D modulator composed of one polarizationbeam splitter, two I/Q modulators, and one polarization beam combiner;multiplexing modulated signals by using mode-multiplexer; andtransmitting the signals over a transmission medium.

A system for transmitting data, including one or more generalizedlow-density parity check (GLDPC) encoders configured to encode one ormore streams of input data, the one or more GLDPC encoders being furtherconfigured to generate GLDPC coded streams using a plurality ofcomponent local codes to increase error correction strength; employsingle-parity checks and two or more local block codes during generationof the GLDPC codes; and enable continuous tuning of code rate using thegenerated GLDPC codes; one or more mappers configured to generate one ormore signals, the mappers being further configured to assign bits of oneor more signals to one or more signal constellations and to associatethe bits of the one or more signals with one or more signalconstellation points; one or more I/Q or 4-D modulators configured tomodulate the signal from the mappers using either one polarization beamsplitter, two I/Q modulators, or one polarization beam combiner; one ormore mode-multiplexers configured to multiplex modulated signals; and atransmission medium configured to transmit the signals.

A system for receiving data, including one or more receivers configuredto receive transmitted signals; one or more demultiplexers, polarizationdiversity coherent detection of the received transmitted signals, anddemodulators/demappers configured to demultiplex, demodulate/demap, andperform; and one or more generalized low-density parity-check (GLDPC)decoders configured to decode the received signals, the one or moreGLDPC decoders being further configured to perform a plurality ofiterations of decoding, and to halt decoding when a valid codeword hasbeen obtained or a predetermined number of iterations is reached.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block/flow diagram illustrating a system/method for datatransport that employs generalized low-density parity-check (GLDPC)codes derived from multiple component codes in accordance with thepresent principles;

FIG. 2 is a block/flow diagram illustrating a system/method for datatransport that employs generalized low-density parity-check (GLDPC)codes derived from multiple component codes in accordance with thepresent principles;

FIG. 3 is a flow diagram illustrating a system/method for data transportgeneralized low-density parity-check (GLDPC) codes derived from multiplecomponent codes in accordance with the present principles; and

FIG. 4 is a block/flow diagram illustrating a system for data transportthat employs generalized low-density parity-check (GLDPC) codes derivedfrom multiple component codes in accordance with the present principles.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In accordance with the present principles, systems and methods areprovided to enable ultra-high speed serial optical transport that mayemploy commercially available equipment operating at lower speed byemploying generalized low-density parity-check (GLDPC) codes derivedfrom multiple component codes. It is noted that GLDPC coding representsan excellent candidate for ultra-high-speed optical transport due itslow decoding complexity and good error performance, in particular forcolumn-weight-3 global codes. However, GLDPC codes based oncolumn-weight-3 LDPC codes exhibit low code rates to be of practicalimportance for ultra-high-speed optical transport. As a compromisingsolution, conventional GLDPC codes based on column-weight-2 global codeshave been studied for use in optical communication. However, this classof GDLPC codes, although of low decoding complexity, has inferiorperformance compared to corresponding LDPC counterparts.

Conventional systems have employed single block-code as a local (e.g.,constituent) code in GLDPC coding. However, to improve error correctionstrength of GLDPC coding, the present principles may employ multiplecomponent local codes (e.g. Hamming, Bose, Chaudhuri, and Hocquenghem(BCH), Reed-Muller (RM) codes, etc.), instead of a single local code.Furthermore, to solve for low code rate problem, the present principlesmay employ a class of GLPDC codes composed of single-parity checks andseveral local block codes.

The maximum a posteriori probability (MAP) decoding of a single-paritycheck code may be trivial, while the overall complexity of MAP decoderof RM codes (e.g., based on fast Walsh-Hadamard transform) may be oforder n log n, where n is the codeword length of RM code. Record codinggains may be obtained from properly designed GLDPC codes, derived frommultiple component codes, according to the present principles.

Before discussing the present principles in detail, it is noted thatseveral recently proposed classes of LDPC codes (e.g., convolutional,staircase, and spatially-coupled codes) may be described using theconcept of GLDPC coding, and as such, the GLDPC coding according to thepresent principles may be used as a unified platform for advanced FECenabling ultra-high speed optical transport. The present principles mayemploy GLDPC codes based on multiple component (local) codes. Forexample, let the parity-check matrices of the l-th local code be denotedby H_(l) (l=1, . . . , L; L-the number of local codes), and let theparity-check matrix of global code be denoted by H_(G). The followingH_(G)-matrix may lead to the generalization of both Tanner and Boutroscodes, and may be given as follows:

Next, the bit nodes in (1) corresponding to the l-th local code (l=1, .. . , L) may be replaced by parity-check matrix of (n₁,k_(l)) local codeH_(l), wherein such a matrix may be denoted by H_(B). In one embodiment,there may be overlap between neighboring two rows in global code, whichmay be different for different neighboring row-pairs. Such obtained codemay be categorized as a staircase-like LDPC code, providing that localcodes are LDPC subcodes. By instead employing Hamming, BCH, and RM codesas local codes, a much stronger GLDPC code can be obtained. Theparity-check matrix of GLDPC code may be obtained as follows:H=[H _(B) ^(T)π_(j)(H _(B))^(T) . . . π_(W−1)(H _(B))^(T)],  (2)where π_(j)(j=1, . . . , W−1) may denote the random-column permutationof H_(B) (T denotes the transposition operation). The decoding of thisGLDPC code can be performed in a conventional manner, and other classesof recently proposed LDPC codes (e.g., convolutional andspatially-coupled) may also be illustrated in a similar fashion.

In one embodiment, to obtain various classes of LDPC codes, the templateparity-check matrix of quasi-cyclic LDPC codes may be employed, and maybe defined as:

$\begin{matrix}{{H = \begin{bmatrix}I & I & I & \ldots & I \\I & P^{S{\lbrack 1\rbrack}} & P^{S{\lbrack 2\rbrack}} & \ldots & P^{S{\lbrack{c - 1}\rbrack}} \\I & P^{2{S{\lbrack 1\rbrack}}} & P^{2{S{\lbrack 2\rbrack}}} & \ldots & P^{2{S{\lbrack{c - 1}\rbrack}}} \\\ldots & \ldots & \ldots & \ldots & \ldots \\I & P^{{({r - 1})}{S{\lbrack 1\rbrack}}} & P^{{({r - 1})}{S{\lbrack 2\rbrack}}} & \ldots & P^{{({r - 1})}{S{\lbrack{c - 1}\rbrack}}}\end{bmatrix}},} & (3)\end{matrix}$where I may be a B×B (B is a prime number) identity matrix, P may be aB×B permutation matrix given by P=(p_(ij))_(B×B), p_(i,j+1)=p_(B,1)=1(zero otherwise), and where r and c represent the number of block-rowsand block-columns, respectively. The powers of permutation matricesdenoted as S[i]; i=0, 1, . . . , c−1; may be chosen appropriately (e.g.,so that cycles of short length (in particular 4 and 6) are avoided.

In one embodiment, the template H-matrix of (column-weight-3,row-weight-5) regular QC code may be given as:

$\begin{matrix}{{H_{t} = \begin{bmatrix}I & I & I & I & I \\I & P^{S{\lbrack 1\rbrack}} & P^{S{\lbrack 2\rbrack}} & P^{S{\lbrack 3\rbrack}} & P^{S{\lbrack 4\rbrack}} \\I & P^{2{S{\lbrack 1\rbrack}}} & P^{2{S{\lbrack 2\rbrack}}} & P^{2{S{\lbrack 3\rbrack}}} & P^{2{S{\lbrack 4\rbrack}}}\end{bmatrix}},} & (4)\end{matrix}$where the global code may be an identity matrix. By interpreting theportions of this template matrix as local codes, a GDLPC code may becreated as follows:

$\begin{matrix}{{H = \begin{bmatrix}I & \; & \; & \; & \; & \; & \; \\P^{S{\lbrack 1\rbrack}} & P^{S{\lbrack 2\rbrack}} & \; & \; & \; & \; & \; \\P^{2{S{\lbrack 1\rbrack}}} & P^{2{S{\lbrack 2\rbrack}}} & P^{2{S{\lbrack 3\rbrack}}} & \; & \; & \; & \; \\\; & I & I & I & \; & \; & \; \\\; & \; & P^{S{\lbrack 3\rbrack}} & P^{S{\lbrack 1\rbrack}} & P^{S{\lbrack 2\rbrack}} & \; & \; \\\; & \; & \; & P^{2{S{\lbrack 1\rbrack}}} & P^{2{S{\lbrack 2\rbrack}}} & P^{2{S{\lbrack 3\rbrack}}} & \; \\\; & \; & \; & \; & I & I & \; \\\; & \; & \; & \; & \; & P^{S{\lbrack 3\rbrack}} & \; \\\; & \; & \; & \; & \; & \; & \ddots\end{bmatrix}},} & (5)\end{matrix}$which may be the convolutional LDPC code of period 4 (e.g., indicatingthat a convolutional code is periodic).

In one embodiment, if the global codes are let to be an all-one columnvector, interpreting the portions of the template matrix as local codes,a GLDPC code may be created as follows:

$\begin{matrix}{{H = \begin{bmatrix}I & {I\;} & \; & \; \\P^{S{\lbrack 1\rbrack}} & P^{S{\lbrack 2\rbrack}} & I & I \\P^{2{S{\lbrack 1\rbrack}}} & P^{2{S{\lbrack 2\rbrack}}} & P^{S{\lbrack 3\rbrack}} & P^{S{\lbrack 4\rbrack}} \\\; & \; & P^{2{S{\lbrack 3\rbrack}}} & P^{2{S{\lbrack 4\rbrack}}}\end{bmatrix}},} & (6)\end{matrix}$which may be a spatially-coupled LDPC code. The staircase-LDPC codes maybe designed in a similar fashion as follows:

$\begin{matrix}{H = {\begin{bmatrix}I & I & I & I & \; & \; & \; & \; \\\; & \; & I & P^{S{\lbrack 1\rbrack}} & P^{S{\lbrack 2\rbrack}} & P^{S{\lbrack 3\rbrack}} & \; & \; \\\; & \; & \; & \; & I & P^{2{S{\lbrack 1\rbrack}}} & P^{2{S{\lbrack 2\rbrack}}} & P^{2{S{\lbrack 3\rbrack}}}\end{bmatrix}.}} & (7)\end{matrix}$

It is noted that the design of spatially coupled LDPC code andstaircase-LDPC codes from the same template-quasi cyclic (QC) LDPC codeis not the unique one. In one embodiment, the decoding can now beperformed in GLDPC fashion by, for example, interpreting the block-rowsas the local codes and applying soft-input soft-output (SISO) decoding.Multiple SISO decoders may operate in parallel, and once SISO decodingis complete, the corresponding log-likelihood ratios (LLRs) may bepassed to global code perform either a message passing method (commonfor LDPC codes), or MAP decoding, depending on the complexity of theglobal code. Thus, the GLDPC codes derived by (2) are inferior to theclass of GLDPC codes by Lentmaier and Zigangirov (LZ-codes). Forsimplicity of illustration, only LZ GLDPC codes will be discussed belowaccording to the present principles, and the LZ-codes discussed may bederived from multiple component codes, although it is noted that anyother codes may also be employed according to the present principles.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable storage medium such as a semiconductor or solid statememory, magnetic tape, a removable computer diskette, a random accessmemory (RAM), a read-only memory (ROM), a rigid magnetic disk and anoptical disk, etc.

A data processing system suitable for storing and/or executing programcode may include at least one processor coupled directly or indirectlyto memory elements through a system bus. The memory elements can includelocal memory employed during actual execution of the program code, bulkstorage, and cache memories which provide temporary storage of at leastsome program code to reduce the number of times code is retrieved frombulk storage during execution. Input/output or I/O devices (includingbut not limited to keyboards, displays, pointing devices, etc.) may becoupled to the system either directly or through intervening I/Ocontrollers.

Network adapters may also be coupled to the system to enable the dataprocessing system to become coupled to other data processing systems orremote printers or storage devices through intervening private or publicnetworks. Modems, cable modem and Ethernet cards are just a few of thecurrently available types of network adapters.

Referring now to FIG. 1, a system for data transport employing multiplecomponent code based generalized low-density parity-check (GLDPC) codes100 to improve error correction (e.g., forward error correction (FEC))is illustratively depicted according to one embodiment of the presentprinciples. In one embodiment, the system 100 includes L component(local) codes 104 (represented by square) and k information bits arerepresented by circle 102. The l-th (l=1, 2, . . . , L) component code(n_(i), k_(l)) is represented by the parity-check matrix H_(l). Theconnections among variable nodes (102) and component code nodes (104)are established based on parity-check matrix of global LDPC code H_(G),represented by block 106. The l-th row of H_(G) corresponds to the l-thcomponent code. The nonzero locations indicate which bit nodes values topass to the l-th code for further encoding. The encoding of local codesis performed iteratively in order (l=1, 2, . . . , L), since a given bitnode can be involved in several component codes. After GLDPC encoding,the codeword is passed to multidimensional coded-modulator, followed bymultidimensional electro-optical modulator, and transmitted over atransmission medium (e.g., single-mode fiber, or spatial divisionmultiplexing (SDM) fiber (e.g., few-mode fiber (FMF), few-core fiber(FCF), or few-mode-few-core fiber (FMFCF)).

Referring now to FIG. 2, a system/method for data transport employingmultiple component code based generalized low-density parity-check(GLDPC) codes to improve error correction (e.g., forward errorcorrection (FEC)) is illustratively depicted according to one embodimentof the present principles. It is noted that LZ-codes (e.g., a class ofGLDPC codes) may be generated starting from global LDPC codes byreplacing every row of a global LDPC code by a parity-check matrix of asingle local code.

However, in one embodiment, a different method is employed according tothe present principles. In this embodiment, to improve the errorcorrection strength of GLDPC coding, multiple component local codes arereceived as input in block 202, and GLDPC codes are generated using themultiple component codes in block 204. The i-th row of a global code maybe replaced by the parity-check matrix of the i-th local (component)code H_(i) according to the present principles. It is noted that aglobal code may include a plurality of rows, and therefore, manymultiple codes may be defined, and if the number of rows in a globalcode is larger than the number of available local codes, the repetitionof certain local codes is unavoidable. It is further noted that therow-weight of the i-th row in global code may be equal to the codewordlength of employed local code n_(i), and that the global LDPC code couldbe either a regular or an irregular LDPC code.

In one embodiment, for ultra-high-speed applications (e.g., beyond 100Gb/s serial optical transport), the use of global LDPC codes ofrow-weight larger than 2 leads to unacceptably low overall code rates ofGLDPC codes. This is one reason why regular (or irregular) LZ codesbased on global codes of column-weight of ≦2 are advantageously employedaccording to the present principles. In one embodiment, by employing thepresent principles to improve the code rate, some of local codes couldbe simple parity-check equations, whose MAP decoding complexity istrivial. For instance, if only single-parity check codes and (n,k) localcode are used in regular GLDPC code design, the corresponding code rateR can be bounded as follows:

$\begin{matrix}{{{1 - \frac{W}{n} - {\frac{W}{d}\left( {1 - \frac{k + 1}{n}} \right)}} \leq R \leq R_{G}},} & (8)\end{matrix}$where W is the column-weight of the global regular code, and parameter ddenotes that the every d-th row in a global code is replaced by (n,k)local code, while the remaining rows from the global code may beinterpreted as single-parity-check codes in GLDPC code. In (8), R_(G)denotes the code rate of global regular code, which may be R_(G)=1−W/n.This GLDPC code design is quite suitable for code-rate adaptation, andan effectively continuous tuning of code rate is possible by varying theparameter d.

In one embodiment, the complexity of decoding of GLDPC codes, when allparity-check equations in the parity-check matrix of the global code aresubstituted with local codes, is of the order (N/n)Σ_(i) n_(i) logn_(i), where N is the codeword length of the global code, n is theaverage row-weight of the global code, and n_(i) is the row-weight ofthe i-th row. On the other hand, the decoding complexity of GLDPC codewith code rate satisfying (8) is of the order (N/d) Σ_(i) n_(i) logn_(i)+(N−N/d)×3, where the second term corresponds to the complexity ofthe parity-check equations. The complexity of the single parity-check isthree additions per local variable node. Since the complexity of asum-product algorithm (typically used in decoding of LDPC codes) isdominated by the check-node update rule, the complexity of thesum-product algorithm (per iteration) will be of the order (N−K)w_(r),where (N,K) are parameters of resulting GLDPC code, and w_(r) is theaverage row-weight of the global code parity-check matrix. Given thefact that resulting GLDPC code is of girth-4 and has huge column-weightit does not make sense at all to use the sum-product algorithm indecoding of resulting GLDPC code, since strictly speaking the resultingGLDPC code is not a low-density one. Instead, the comparison can be madewith respect to a reasonable complexity LDPC (N_(LDPC), K_(LDPC)) codeof large (high) girth.

The complexity of the GLDPC codes according to one embodiment of thepresent principles, with multiple RM component codes (when thecomplexity of the parity-check equations can be ignored) may be,therefore, (N_(LDPC)−K_(LDPC))w_(r)/[(N/d) Σ_(i)n_(i) log₂ n_(i)] timeslower than that of a competitive LDPC (N_(LDPC), K_(LDPC)) code ofrow-weight w_(r). When single-parity-checks dominate over other localcodes, the complexity of parity-check codes must be taken into account.Given that the complexity of variable-nodes update rule in an LDPC codeis given by N_(LDPC)w_(c), where we is the column-weight of theparity-check matrix of LDPC code, while the complexity of variablesLLRs' update is N_(LDPC) (w_(c)+1), the complexity ratio (CR) of LDPCdecoder complexity over GLDPC decoder complexity [satisfying theinequalities (1)] can be defined as:

$\begin{matrix}{{{C\; R} = {\frac{{\left( {N_{LDPC} - K_{LDPC}} \right)w_{r}} + {N_{LDPC}\left( {{2w_{c}} + 1} \right)}}{{\left( {N/d} \right){\sum\limits_{i}\;{n_{i}\;\log_{2}\; n_{i}}}} + {\left( {N - {N/d}} \right) \times 3}} \times \frac{t_{LDPC}}{t_{GLDPC}}}},} & (9)\end{matrix}$where t_(LDPC) and t_(GLDPC) denote the number of iterations in LDPC andGLDPC codes, respectively.

In one embodiment, Hamming, BCH, and/or RM codes may be employed asmultiple component codes in block 206, and single-parity checks and oneor more block codes may be included in the class of GLDPC codes, and asMAP decoding of single parity-checks may be trivial, while the overallcomplexity of MAP decoder for RM code based on FWHT may be of order nlog n, this class of GLDPC codes may be employed effectively forultra-high-speed implementation at least because of its low complexitylevel as compared to conventional LDPC counterparts. A continuous, ornearly continuous tuning of code rate may be performed in block 208, andthe GLDPC codes generated according to the present principles may beemployed in both multilevel and multidimensional coded-modulations inblock 210.

In one embodiment, signals may be generated using one or more mappers,and bits of signals may be assigned to one or more signal constellationsin block 212. Signals may be transmitted over a transmission medium(e.g., FMF) in block 214, and the transmitted signals may be received bya receiver and decoded using one or more GLDPC decoders in block 216. Aplurality of iterations of decoding using a subnode update rule and aspecialized low-complexity GLDPC decoder (e.g., Ashikhmin-LytsinDecoder) may be performed in block 218, and decoding may halt when avalid codeword has been obtained or when a predetermined (e.g., maximum)number of iterations has been reached in block 220.

The decoding principle of the GDLPC codes according to the presentprinciples can be described as follows. Let x=(x_(v))_(b≦v≦s) be acodeword, and let H_(G)=(h_(s,v))_(b×n), be the parity-check matrix of aglobal code (with b and n representing the dimensions of H_(G)). Eachrow s of this matrix represents a subcode node and every column v avariable (bit) node in corresponding bipartite graph. An edge connectingvertices s and v exists if h_(s,v)=1, i.e. if variable v has beeninvolved in subcode s. The parity-check matrices of local codes denotedby H_(s)(s=1, . . . , S). Obviously, the subcode node s degree must beidentical to the number of columns in local code H_(s). The positions ofones in the s-the row of H_(G) determine the variables passed to thelocal decoder H_(s). The decoding method for LZ-codes with multiplecomponent codes can be summarized as follows.

Initialization step. The prior information of the bit at position v,μ_(v) ⁽⁰⁾, is determined as

$\begin{matrix}{{\mu_{v}^{(0)} = {\log\left\lbrack {\log\left( \frac{P\;{r\left( {v = {0❘y_{v}}} \right)}}{P\;{r\left( {v = {1❘y_{v}}} \right)}} \right)} \right\rbrack}},} & (10)\end{matrix}$with y_(v) is the sample that corresponds to x_(v). The messages passedfrom variable node v to subcode node s in the bipartite graph, λ_(v,s)⁽⁰⁾, are initialized to μ_(v) ⁽⁰⁾.Suhnode update rule. In the i-th iteration, the messages to be passedfrom subcode node s to bit node v, Λ_(s,v) ^((i)), are obtained as theoutputs of corresponding specialized low-complexity GLDPC decoder (e.g.,Ashikhmin-Lytsin decoder), operating on the local codes described by theparity-check matrices H_(s) (s=1, . . . , S).Variable node update rule. Messages to be passed from bit node v tosubcode node s, λ_(v,s) ^((i)), are updated according to:

$\begin{matrix}{\lambda_{v,s}^{(i)} = {\mu_{v}^{(0)} + {\sum\limits_{s^{\prime} \neq s}\;{\Lambda_{s^{\prime},v}^{(i)}.}}}} & (11)\end{matrix}$Bit decisions. The last step in the j-th iteration is to compute updatedLLRs μ_(v) ^((j)) according to:μ_(v) ^((i))=μ_(v) ⁽⁰⁾+Σ_(x)Λ_(x,v) ^((j)).  (12)For each bit x_(v) the estimation is made according to

$\begin{matrix}{{\hat{x}}_{v} = \left\{ {\begin{matrix}{1,} & {{{if}\mspace{14mu}\mu_{v}^{(j)}} < 0} \\{0,} & {otherwise}\end{matrix}.} \right.} & (13)\end{matrix}$Decoding may halt when a valid codeword has been obtained or apredetermined maximum number of iteration has been reached.

It is noted that while the above configuration and GLDPC codes areillustratively depicted according to embodiments of the presentprinciples, other sorts of configurations and GLDPC codes arecontemplated, and may be employed according to the present principles.

Referring now to FIG. 3, plots of graph descriptions for data transportemploying multiple component code based generalized low-densityparity-check (GLDPC) codes to improve error correction (e.g., forwarderror correction (FEC)) is illustratively depicted according to oneembodiment of the present principles. In one embodiment, as anillustration, a GLDPC code composed of, for example, RM(1,3) andsingle-parity checks is shown. Component (local codes) may be based onRM(1,3), designated by trellis description 301, and single-parityRM(2,3) codes, designated by trellis description 303, while the globalcode may be based on a bipartite (e.g., Tanner) graph of girth-10,column-weight-3, QC-LDPC (3544,2215) code (with permutation block sizeof 443), designated by 305. In one embodiment, point 310 may representthe bit node in a global code and square 312 the component code.

In one embodiment, if the every 100-th row in global code is replaced byRM(1,3) code, the corresponding GDLPC code may be of rate 0.614. Theupper bound of this two-component-RM-codes-based-GLDPC code may be0.625. Decoding of component RM(1,3) and RM(2,3) codes may be based onthe fast Hadamard-Walsh transform (FHWT). The bit log-likelihood ratiosmay then be passed to the global code, which may apply a variable-nodeupdate rule. The overall decoding method of GLDPC code is similar to thesum-product algorithm in which the check-nodes update rule get replacedby decoding of local codes. When every 100-th component code is based onRM(1,3) code, the complexity of GLDPC decoding is in order of(2176/100)×8 log₂ 8 operations per sub-node (where the decodingcomplexity of parity-check code is trivial, and may be ignored).

A conventional LDPC code may have the girth-8 and column-weight-5,row-weight-13, with the complexity of check-node update rule being(7241−4456)×13, for example. Therefore, the overall complexity of GLDPCcode from this embodiment according to the present principles isapproximately 70 times lower than that of conventional LDPC codes. It isnoted that this example has been provided for illustrative purposes, andthat other configurations of rows, rates, etc. may also be employedaccording to the present principles.

It is noted that the present principles may be employed to improveoverall BER performance of LDPC codes, by employing the GLDPC codes withmultiple component (local) codes. These component local codes are takenfrom, for example, the following classes of codes, to enable lowdecoding complexity of GLDPC codes: Hamming, BCH and RM codes as well ascorresponding codes derived from these codes (various extended,shortened versions, etc.). To solve for low code rate problem, a classof GLPDC codes employed according to one embodiment may be composed ofsingle-parity checks and several local block codes.

Since the MAP decoding of a single-parity check is trivial, while theoverall complexity of MAP decoder for RM code, based on FWHT is of ordern log n, this class of GLPDC codes according to the present principlesenables ultra-high-speed implementation, as the decoding complexity ismuch lower compared to LDPC counterparts.

In one embodiment, record coding gains have been shown by employingGLDPC codes derived from multiple component codes according to thepresent principles. For example, the GLDPC (59993, 49397, 0.823) mayhave the NCG of 12 dB at BER of 10⁻¹⁵, representing the largest everreported NCG for 21.45% overhead code. We have shown that the proposedclass of GLDPC codes, composed of multiple local codes and single-paritychecks, enables almost continuous tuning of code rate. Therefore, theproposed class of GLDPC coding is extremely suitable for rate adaptivecoding as well as adaptive modulation and coding.

Referring now to FIG. 4, a high level illustration of a system for datatransport employing multiple component code based generalizedlow-density parity-check (GLDPC) codes 100 to improve error correction(e.g., forward error correction (FEC)) is illustratively depictedaccording to one embodiment of the present principles. In oneembodiment, input data 402 may be received into a transmitter 401, andmay be encoded using one or more GLDPC encoders in block 404. The datamay be mapped to a given constellation and modulated in block 406 usinga mapper followed by electro-optical modulator, and may be multiplexedusing either polarization division multiplexer or mode-multiplexer inblock 408. The optically multiplexed signals may be transmitted over atransmission medium 410 (e.g., SMF or FMF). The transmitted signals maybe received by a receiver 403, and the signals may be demultiplexedusing a modedemultiplexer followed by polarization diversity coherentdetector in block 412, demodulated and demapped using a demodulator &demapper in block 414. The signals demodulation by an a posterioriprobability demodulator/demapper in block 414, and may then be decodedusing one or more GLDPC decoders in block 416. The decoding may continueuntil a valid codeword has been obtained or a predetermined (e.g.,maximum) number of iterations has been reached.

It is noted that although the above configuration is illustrativelydepicted according to the present principles, other sorts ofconfigurations may also be employed according to the present principles.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. Additional information is provided in anappendix to the application entitled, “Additional Information”. It is tobe understood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that thoseskilled in the art may implement various modifications without departingfrom the scope and spirit of the invention. Those skilled in the artcould implement various other feature combinations without departingfrom the scope and spirit of the invention. Having thus describedaspects of the invention, with the details and particularity required bythe patent laws, what is claimed and desired protected by Letters Patentis set forth in the appended claims.

What is claimed is:
 1. A method for data transport, comprising: encodingone or more streams of input data using one or more generalizedlow-density parity check (GLDPC) encoders, the one or more GLDPCencoders being configured to: generate GLDPC coded streams byconcurrently using two or more types of component local codes toincrease error correction strength, the plurality of types of componentlocal codes including at least two of Hamming; Bose, Chaudhuri, andHocquenghem (BCH); or Reed-Muller (RM) codes; employ single-paritychecks and two or more local block codes during generation of the GLDPCcoded streams; and enable continuous tuning of code rate using thegenerated GLDPC coded streams; generating one or more signals from theGLDPC coded streams using one or more mappers, the mappers configured toassign bits of the one or more signals from the GLDPC coded streams toone or more signal constellations and to associate the bits of the oneor more signals with one or more signal constellation points; modulatingthe signal from the mappers using either In-phase/Quadrature (I/Q) or4-Dimensional (4D) modulators composed of one polarization beamsplitter, two I/Q modulators, and one polarization beam combiner;multiplexing modulated signals by using one or more mode-multiplexers;and transmitting the modulated multiplexed signals over a transmissionmedium.
 2. The method as recited in claim 1, wherein the GLDPC codedstreams are employed for rate adaptive coding.
 3. The method as recitedin claim 1, wherein the GLDPC coded streams are employed for adaptivemodulation and coding.
 4. The method as recited in claim 1, wherein theGLDPC coded streams are employed in multilevel and multidimensionalcoded-modulations.
 5. The method as recited in claim 1, wherein theGLDPC coded streams employ one or more global LDPC codes, the globalLDPC codes being based on either regular or irregular LDPC codes.
 6. Themethod as recited in claim 5, wherein an i-th row of the global LDPCcodes is replaced by a parity check matrix of an i-th local code.
 7. Themethod as recited in claim 1, further comprising: receiving thetransmitted signals using one or more receivers; demultiplexing followedby polarization diversity coherent detection of the received signals anddemodulating/demapping using one or more demultiplexers, one or morecoherent detectors, and one or more demodulators/demappers; decoding thedemodulated/demapped signals using one or more GLDPC decoders, the oneor more GLDPC decoders being configured to perform a plurality ofiterations of decoding; and halting decoding when a valid codeword hasbeen obtained or a predetermined number of iterations is reached.
 8. Themethod as recited in claim 7, wherein the plurality of iterations ofdecoding is performed using a subnode update rule and a specializedlow-complexity Ashikhmin-Lytsin decoder, wherein the Ashikhmin-Lytsindecoder operates on local codes described by parity check matrices.
 9. Asystem for transmitting data, comprising: one or more generalizedlow-density parity check (GLDPC) encoders configured to encode one ormore streams of input data, the one or more GLDPC encoders being furtherconfigured to: generate GLDPC coded streams by concurrently using two ormore types of component local codes to increase error correctionstrength, the plurality of types of component local codes including atleast two of Hamming; Bose, Chaudhuri, and Hocquenghem (BCH); orReed-Muller (RM) codes; employ single-parity checks and two or morelocal block codes during generation of the GLDPC coded streams; andenable continuous tuning of code rate using the generated GLDPC codedstreams; one or more mappers configured to generate one or more signalsfrom the GLDPC coded streams, the mappers being further configured toassign bits of the one or more signals from the GLDPC coded streams toone or more signal constellations and to associate the bits of the oneor more signals with one or more signal constellation points; one ormore In-phase/Quadrature (I/Q) or 4-Dimensional (4D) modulatorsconfigured to modulate the one or more signals from the one or moremappers using either one polarization beam splitter, two I/Q modulators,or one polarization beam combiner; one or more mode-multiplexersconfigured to multiplex modulated signals; and a transmission mediumconfigured to transmit the modulated multiplexed signals.
 10. The systemas recited in claim 9, wherein the GLDPC coded streams are employed forrate adaptive coding.
 11. The system as recited in claim 9, wherein theGLDPC coded streams are employed for adaptive modulation and coding. 12.The system as recited in claim 9, wherein the GLDPC coded streams areemployed in multilevel and multidimensional coded-modulations.
 13. Thesystem as recited in claim 9, wherein the GLDPC coded streams employ oneor more global LDPC codes, the one or more global LDPC codes being basedon either regular or irregular LDPC codes.
 14. The system as recited inclaim 13, wherein an i-th row of the one or more global LDPC codes isreplaced by a parity check matrix of an i-th local code.
 15. A systemfor receiving data, comprising: one or more receivers configured toreceive transmitted modulated multiplexed signals; one or moredemultiplexers, one or more coherent detectors, and one or moredemodulators/demappers configured to: demultiplex, perform polarizationdiversity coherent detection of the received transmitted modulatedmultiplexed signals, and demodulate/demap the received transmittedmodulated multiplexed signals, respectively; and one or more generalizedlow-density parity-check (GLDPC) decoders configured to decode thedemodulated/demapped signals from GLDPC coded streams generated byconcurrently using two of more types of component local codes, the oneor more GLDPC decoders being further configured to perform a pluralityof iterations of decoding, and to halt decoding when a valid codewordhas been obtained or a predetermined number of iterations is reached,the plurality of types of component local codes including at least twoof Hamming; Bose, Chaudhuri, and Hocquenghem (BCH); or Reed-Muller (RM)codes.
 16. The system as recited in claim 15, wherein the plurality ofiterations of decoding is performed using a subnode update rule and aspecialized low-complexity Ashikhmin-Lytsin decoder, wherein thespecialized low-complexity Ashikhmin-Lytsin decoder operates on localcodes described by parity check matrices.
 17. The system as recited inclaim 15, wherein the one or more GLDPC decoders are employed for rateadaptive coding.
 18. The system as recited in claim 15, wherein the oneor more GLDPC decoders are employed in multilevel and multidimensionalcoded-modulations.